You need to look at 2x2s and which numbers can reach them. For example, above the 4 and just to the right - what can reach there? And if the 4 goes up too far, it cuts the shaded squares off from one another. And what can reach the top centre of the grid, one square down?
From this you can place most of the 12, and work out how the 4 goes. This eventually forces the bottom-right 6, and from there you can flow anticlockwise around the grid - and also then finalise the 12 at a certain point.
It's a very difficult puzzle, but you can solve all of it without having to guess if you use the above logic.
Posted 2nd Mar 2020 at 19:26 Last edited by JoergWausW 2nd Mar 2020 at 19:27
I think this is a pretty difficult puzzle that you have to approach by more complex strategies if you don't want to just try. And I think in the end I made a probable guess, too.
The yellow 6 can only reach that far. Below the end of that yellow area are two orange cells (not yet shaded). These two can't be both black, so the 12 area has to go here. Nothing else can. So those four white cells in row 1 are fixed. Not more. You might think the right one of the two has to be white, but that cell might be needed for connecting black areas around the top right 1. Then the 12 area expands one cell more to the left and then one cell down.
Same applies in the bottom right corner: 4 and 6 can't reach enough to the top. Again, there would be a block of 4 black cells if the 12 doesn't go there.
Note: the 4 area can't be that way, because it is blocking of a black cell in the middle. So the 4 has to expand at least one cell in a different direction...
I was surprised to see that you can recolor the numbered cells. But it doesn't work with shaded colors. Great programming!
Posted 3rd Mar 2020 at 10:35
Rachel Rated puzzle: HardCompletion time: 21:54
Thank you both for your help - Joerg your diagram was great, helped me get started. Although I had to guess again at the end but you both reminded me to focus on the 2x2 blacks. Thanks.
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Last edited by gareth 2nd Mar 2020 at 19:24
From this you can place most of the 12, and work out how the 4 goes. This eventually forces the bottom-right 6, and from there you can flow anticlockwise around the grid - and also then finalise the 12 at a certain point.
It's a very difficult puzzle, but you can solve all of it without having to guess if you use the above logic.
Last edited by JoergWausW 2nd Mar 2020 at 19:27
Look at this picture:
Pic Hint
The yellow 6 can only reach that far. Below the end of that yellow area are two orange cells (not yet shaded). These two can't be both black, so the 12 area has to go here. Nothing else can. So those four white cells in row 1 are fixed. Not more. You might think the right one of the two has to be white, but that cell might be needed for connecting black areas around the top right 1. Then the 12 area expands one cell more to the left and then one cell down.
Same applies in the bottom right corner: 4 and 6 can't reach enough to the top. Again, there would be a block of 4 black cells if the 12 doesn't go there.
Note: the 4 area can't be that way, because it is blocking of a black cell in the middle. So the 4 has to expand at least one cell in a different direction...
You can do the same steps with the 9 going north.
Maybe this helps you getting started.
edit to add: gareth beat me by two minutes...
I was surprised to see that you can recolor the numbered cells. But it doesn't work with shaded colors. Great programming!
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